An Estimate of Tidal and Non-Tidal Modulations of Plate Subduction

Tanaka et al. Earth, Planets and Space (2015) 67:141 DOI 10.1186/s40623-015-0311-2

FRONTIER LETTER Open Access An estimate of tidal and non-tidal modulations of plate subduction speed in the transition zone in the Tokai district Yoshiyuki Tanaka1*, Suguru Yabe2 and Satoshi Ide2

Abstract Non-volcanic tremors and slow slip events in subduction zones have been found to be triggered by small external stress disturbances, as demonstrated by the synchronization of temporal variations in tremor rate with diurnal and semi-diurnal tides. Therefore, long-term variations in tremor rate might be predicted by amplitude modulations of diurnal and semi-diurnal tides at decadal time scales. Given that tremors and slow slips are shear slip on the plate boundary, their long-term variations must be associated with fluctuations in plate subduction speed below the seismogenic zone. In previous work, we showed a good correlation between long-term seismicity and empirically calculated tremor rate based on observed tidal levels in the Nankai region, western Japan. Here, we present an improved method of modeling long-term slip rate fluctuation based on the calculation of Coulomb stress due to ocean and solid earth tides on the plate interface. We also include the effects of non-tidal ocean variations, such as the Pacific Decadal Oscillation and the Kuroshio Current, employing an ocean model developed by the Japan Meteorological Agency. We apply the method to the Tokai district, where the effects of the Kuroshio Current are large, and demonstrate the importance of considering non-tidal effects. Our calculated slip rate fluctuations could amount to 1 mm/year in decadal scales, and periods with faster rates partly corresponded to variations in seismicity. Slow slip events in the study region weakly corresponded to times of higher stress. Keywords: Tides; Slow slip; Tremors; Earthquake; Seismicity; Crustal deformation; Ocean bottom pressure; Pacific Decadal Oscillation; Kuroshio Current

Findings unstable slip. Below the transition zone, slip is always stable, Introduction and the oceanic plate is subducted at a constant velocity. In Recent seismological and geodetic observations have thetransitionzone,thepresenceofhigh-pressurefluids revealed diverse shear slip patterns on plate subduc- due to dehydration of the subducted slab reduces the effect- tion interfaces (Ide et al. 2007a; Ide et al. 2007b), in- ive normal stress (e.g., Kodaira et al. 2004; Peacock 2009). cluding non-volcanic tremors and slow slip events In such cases, a conditionally stable regime can exist, (SSEs) (Obara 2002; Shelly et al. 2006, 2007; Schwartz and even small stress disturbances can trigger tremors and Rokosky 2007; Beroza and Ide 2011; Vidale and and SSEs, which are caused by remote earthquakes and di- Houston 2012). These events occur in the transition urnal and semi-diurnal tides (e.g., Miyazawa and Mori zone at depths of 30–40 km, where the frictional property 2006; Nakata et al. 2008; Rubinstein et al. 2008; Lambert on the plate interface changes from unstable to stable et al. 2009; Houston 2015). (Scholz 2002). In the seismogenic zone located just above Stress disturbances due to tremors and SSEs can trigger a the transition zone, the plate interface is locked partially, major rupture on the plate boundary by providing a final and stress accumulated due to plate motion releases with push (Dragert et al. 2004; Beroza and Ide 2011), and interactions between these slow events and the major rupture * Correspondence: [email protected] zone have been actively studied using numerical simula- 1Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku tions (e.g., Matsuzawa et al. 2010; Segall and Bradley 2012). 113-0032, Tokyo To perform such simulations, the frictional properties on Full list of author information is available at the end of the article

© 2015 Tanaka et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 2 of 11

the plate boundary must be known. One advantage of tremor rate was dominated by an 18.61-year periodic vari- observing the tidal responses of tremors is that a por- ation, which was generated by modulations of diurnal and tion of the frictional properties in the transition zone semi-diurnal tides. Long-term changes were well correlated at large spatial scales can be inferred, which is difficult with background seismicity during the period spanning to determine using laboratory experiments. The obtained from 1965 to 2010 in the Nankai Trough. Historical large properties can also be employed in numerical simulations earthquakes in this region also tended to occur when of earthquake cycles by assimilating observational data the predicted tremor activity with the 18.61-year period (e.g., Hori et al. 2014), which allows for more precise was high (IT2014). long-term forecasts of large earthquakes in each antic- However, in IT2014, tidal and non-tidal effects were not ipated region. In addition, tidal response measurement separated, and steric components were included because is useful for precisely monitoring small episodic stress the model was based on observational tide-level data. In changes (Nakata et al. 2008). this study, the effects of non-tidal variations in OBP on the On the other hand, some studies have reported the pres- slip rate in the transition zone were calculated for the first ence of seasonality and possibility of decadal time- time. For this estimate, a slip response model was applied scale periodicity in the seismicity of large earthquakes to the Tokai district as an example. Fluctuations of the slip in Japan (e.g., Ohtake and Nakahara 1999; Heki 2003; rates were demonstrated, and the importance of including Tanaka 2014). These statistical behaviors indicate the non-tidal effects in comparisons with variations in seis- presence of wide-area stress disturbances, and the ef- micity was noted. fects of these disturbances on the seismogenic zone have been investigated. Currently, only Heki (2003) has suc- cessfully explained the seasonality in northern Japan quan- Methods titatively by using a snow-load model. The effects due to Method for computing slip rate seasonal variations in atmospheric pressure are too small IT2014 presented the idea that tremors triggered by tides to trigger earthquakes (Ohtake and Nakahara 1999). Heki promote plate subduction in the tremor zone (Ide et al. (2004) mentioned that ocean loading models have unce- 2007b), which activates seismicity of shallower earth- rtainties due to steric (i.e., irrelevant with mass changes) quakes. In contrast to Beeler and Lockner (2003), who components and that in situ observations of ocean bottom reported that diurnal tides cannot trigger earthquakes pressure (OBP) are necessary for its correct estimation. based on data from laboratory experiments, tremors were Kataoka (2007) estimated seasonal variations in OBP by found to show tidal sensitivities at such high frequencies in using the Estimating the Circulation and Climate of the the Nankai Trough (Yabe et al. 2014), which can indirectly Ocean (ECCO; http://www.ecco-group.org) model and trigger earthquakes. In the current study, this idea is gener- concluded that the amplitudes are insufficient for trig- alized under the assumption that plate subduction speed in gering earthquakes. Currently, such external stress distur- the transition zone, including in slow slip areas, changes bances due to climatic effects have not been incorporated due to external forces. However, to prove that fluctuations in the above numerical simulations of earthquake cycles. in subduction speed below the seismogenic zone can trig- However, in the abovementioned studies, which attempted ger earthquakes, quantitative simulations, such as those to explain the periodicities in seismicity, the high sensitivity made by Hirose and Maeda (2013), would be necessary to of the transition zone to external stress disturbances calculate the 3-D stress distribution on the plate interface. was neglected. When considering their effects on the The stress behaviors would strongly depend on given transition zone, it is possible that smaller stress distur- frictional parameters, and enormous efforts are needed bances trigger tremors and SSEs, which trigger earthquakes. to reveal the parameter sensitivity. In this paper, as a first However, the long-term variations in the occurrence step in producing such simulations, the influences of ex- of tremors and SSEs were not studied until recently. ternal forces, which serve as inputs, are estimated using Pollitz et al. (2013) applied a hydrologic-loading model the empirical model from IT2014, with the number of pa- to explain the periodicity of slow events and the departures rameters being kept small. from periodicity at Vancouver Island, which lies in the The Tokai district is located on the east end of the Cascadia subduction zone. Ide and Tanaka (2014) (ab- Nankai Trough, where the Philippine Sea Plate subducts breviated as IT2014 hereafter) reported the possibility beneath the Eurasian (Amurian) Plate (Fig. 1a), which that tides could trigger tremors at the seasonal scale by ap- is magnified in Fig. 1b. The anticipated source area of a plying an empirical relationship between observed tremor megathrust earthquake is surrounded by the thick black rates and tide-gauge records at Seto Inland Sea. Fur- curve. The black dots and the green circle denote the thermore, IT2014 estimated a multi-decadal variation epicenters of tremors (Idehara et al. 2014) and the area in tremor rate by focusing on long-term modulations of where a large slip occurred due to a long-term SSE from tidal amplitudes (Section 4.2.2 in Pugh 1987). The predicted 2000 to 2006, respectively. Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 3 of 11

(a) (b)

Fig. 1 The location of the Tokai district wheretheslipratewasestimated.a The blue curves denote the depth contours of the Philippine Sea Plates for 20, 30, and 40 km. The green stars denote the epicenters of historical large earthquakes with M > 7.5 (Set C in Tanaka 2014). The light blue circle represents a stationary cold-water mass, which appears when large-scale meandering of the Kuroshio Current occurs. b The thick black curve denotes the anticipated source area of a megathrust earthquake. The black dots and the green circle denote the epicenters of the tremors (Idehara et al. 2014) and the area where a large slip occurred due to a long-term slow slip event from 2000 to 2006, respectively. The solid earth and ocean tides along the red vertical line were compared in Fig. 2a. The slip rate at site H1 was mainly estimated. The ocean bottom pressures at H2–6 are shown in Fig. 3b. c, d The epicenters and magnitudes of small earthquakes with M > 3.5 in the Tokai area, for which the background seismicity from Fig. 4a was inferred. The events took place in anareawithin150kmfromtheSurugaTroughinthedirectionofsubduction(surroundedbythered diamond in (c))

Although IT2014 considered only the response of the characteristic distance associated with the decay of the tremor zone, our model considered the following three state variable, which has not been constrained well in regions on the plate interface: I: seismogenic zone with geologically relevant settings and scales. The estimated A − B<0, including the source area of a megathrust slip rates depend on the assumed A–B and V0,which event; II: shallower (but deeper than the seismogenic can be high or low. Nevertheless, comparing results includ- zone) regions with A − B > 0, including the slow slip area; ing and excluding the non-tidal effects reveals which is and III: deeper regions with A − B >0, including the tremor more dominant in a relative sense when variations in the zone. As in IT2014, slip responses can be expressed as state variable can be regarded as sufficiently slow.

0 V i ¼ V i expðÞΔCFSi=½Ai−Bi ð1Þ Method for computing stress Stress tensors on the plate interface were computed where i =1–3 denotes the index of the three regions, using Green’s functions from Okubo and Tsuji (2001). and V and V0 denote the slip rate and the average slip rate PREM (Dziewonski and Anderson 1981) was employed of each region when external stresses are zero, respectively. for density and elastic structure. The tidal potential of ΔCFS represents the Coulomb failure stress (Scholz 2002) Tamura (1987) and the SPOTL software (Agnew 2012), on the plate interface (ΔCFS > 0 promotes slip), which which incorporates the regional ocean tide model of results from solid earth and ocean tides (Tsuruoka et al. GOTIC2 (Matsumoto et al. 2000), were used to calculate 1995) and from non-tidal variations in OBP. the hourly solid earth and ocean tides, respectively. Non- The slip behavior of Eq. (1) takes the same form as in the tidal variations in OBP were estimated using the data as- steady state (e.g., Nagata et al. 2012); the validity of neglect- similation model of the Meteorological Research Institute ing temporal variations in the state variable depends on the of Japan (Usui et al. 2006). The model input data included Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 4 of 11

V 0 ¼ = daily sea level atmospheric data, such as wind stress, for 2 4cm year. By observing short-term tidal re- rainfall, and thermal fluxes of JRA-25/JCDAS (Onogi et al. sponses, Yabe et al. (2014) found that A − B in Eq. (1) 2007). Temperature and salinity profiles and sea surface was 2–3 kPa in almost all of the tremor zones in the height (SSH) based on in situ and satellite observations are Nankai Trough. By contrast, A − B in the slow slip assimilated. A reanalysis of OBP from 1980 on grid points area was set to −17 kPa by Hirose and Maeda (2013) of 0.1 × 0.1 is available. The spatial resolution of the model to simulate SSE recurrence and the main ruptures in is set sufficiently high to reproduce the variations in the the Tokai area, which were based on a rate- and state- Kuroshio Current. Thus, it is expected that a more realistic dependent law. However, the chosen A − B magnitude OBP is obtained than by using the ECCO, which has lower is not unique because slip behaviors also depend on the spatial resolution. The same Green’sfunctionasforthe characteristic distances discussed above. In this study, the ocean tides was used to calculate stress tensors. magnitude was set to a similar value as in Yabe et al. ΔCFS was calculated from the obtained stress tensors (2014) (A − B = 2 kPa) because the tremor zone and the while considering the geometry of the plate boundary slow slip area were adjacent to each other. The case of (Baba et al. 2002; Nakajima and Hasegawa 2007; Hirose A − B in the slow slip area being negative (conditionally et al. 2008). The frictional coefficient μ in ΔCFS was set to stable) will be discussed later. 0.2 throughout the current study. A similar value was ob- The slip rates were converted to rates of stress change Δ tained in Cascadia (Houston 2015). Hereafter, the CFS at the lower end of region I, assuming K12 = −8 MPa/m caused by solid earth and ocean tides, the sum of these two in Eq. (2). The value of K12 was calculated by applying ΔCFSS and the non-tidal effects are abbreviated as ΔCFSS, the method of Okada (1992) to a 2-D plate interface with Δ Δ Δ CFSO, CFSS+O,and CFSNT, respectively. a dip angle of 17°, assuming that K12 represented the response at H1 (depth 25 km) to a uniform slip on region II, Loading effects on asperities occupying depths from 25 to 35 km. The strike compo- The temporal variations in the stress in the seismogenic nent of the slip was neglected, and isotropic elasticity was zone (region I) can be represented as assumed. X d 3 ÀÁd τ ¼ K i V pl−V i þ ΔCFS ð2Þ dt 1 i¼1 1 dt 1 Earthquakes and SSEs in the Tokai district The computed slip and stress rates were compared in the “Results and discussion” section using the following data. Figure 1c, d shows the seismicity of shallower earthquakes where K1i denotes the elastic Green’s function (e.g., Hirose with M > 3.5. In this area, most events occurred off of the and Maeda 2013). Of the four terms on the right-hand side plate interface. The principal cause of these events is con- V 0 of Eq. (2), the second term is the most important. 1 ap- sidered to be stress accumulation due to plate motion, V 0 pears in the first term after applying Eq. (1). 1 represents and it is expected that a faster slip rate enhances inter- thesliprateintheseismogeniczoneandismuchsmaller plate coupling and corresponds to higher seismicity. V 0 V 0 V 0 ¼ than 2 and 3 ( 1 0 if fully locked). Moreover, the The long-term background seismicity corresponding to shear stress in the seismogenic zone generated by unit these events was obtained by the declustering method slip on region II is larger than that from region III from Ide (2013). (K12 ≪ K13 < 0) because the regions I and II are con- Mogi (1969) noted the seasonality of great earthquakes in tiguous. In addition, the amplitudes of ΔCFS2 near the Nankai Trough. In the Tokai district, earthquakes oc- the coast are larger than ΔCFS3, which is located below curred on Feb. 3, 1605, Oct. 28, 1707, and Dec. 23, 1854. land. For example, Fig. 2a shows the amplitudes of ΔCFSS The occurrence months of these events were compared and ΔCFSO on Jan. 1, 1980, along the N-S line from Fig. 1b. with seasonal variations in the slip rates. The background The effects of ocean tides were observed to decay rapidly seismicity of the shallower earthquakes did not show sea- as the distance from the coast increased, whereas the ef- sonal variations at a statistically significant level. fects of solid earth tides were almost constant. ΔCFSO and Long-term SSEs occurred during the early 1980s, late ΔCFSS+O almost agree in phase, implying that the sum of 1980s, the first half of the 2000s (e.g., Kobayashi 2014) and the effects of solid earth and ocean tides also decreases to- from Nov. 2013 to the time of this writing (Figs. 65 and 66 ward the north. in Geographical Information Authority of Japan 2015). Recurrence intervals of ~10 years can be reproduced by Model parameters numerical simulation (Hirose and Maeda 2013). However, AtthesitemarkedbyH1,ΔCFS was calculated using why these slips occurred during these periods has not been dip, strike, and rake angles of 17°, 250°, and 140°, re- explained. Slip and stress rates were also compared with spectively. The slip rate was calculated using Eq. (1) the occurrences of these events. Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 5 of 11

(a) (b)

(e) (f)

(g) (h)

(i) (j)

Fig. 2 Changes in stress and slip rate estimated at H1 on the plate interface caused by tides and non-tidal variations in ocean bottom pressure (OBP). a A comparison in peak-to-peak amplitudes in ΔCFS between solid earth and ocean tides on Jan. 1, 1980, along the red line in Fig. 1b. b, c The red and blue lines denote ΔCFS caused by ocean tides and that caused by the sum of solid earth and ocean tides, respectively. d, e Hourly, daily, and monthly slip rates calculated using Eq. (1) with ΔCFS being caused by the sum of solid earth and ocean tides shown in (c). f ΔCFS caused by the non-tidal variation in OBP in Fig. 3b. The spatial distribution of OBP near the coast was considered in computing ΔCFS at H1. g, h Hourly, daily, and monthly slip rates calculated using Eq. (1), with ΔCFS being caused by the sum of solid earth and ocean tides and the non-tidal (NT) variation in (f). i, j Thesameas(f, h), but the horizontal axis denotes months, and the results from 1980 to 2013 are cyclically superimposed

Results and discussion an order of magnitude smaller than ΔCFSS+O (blue). The The effects of tidal modulations on ΔCFS and slip rate half amplitudes of ΔCFSS+O were 0.4–1.2 kPa, which were Figure 2b shows the hourly ΔCFS caused by tides between almostthesameasthoseestimatedfortheNankaiTrough 1980 and 1981 at H1. At the inland H1, ΔCFSO (red) was by Nakata et al. (2008). In the time-series plot of ΔCFSS+O, Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 6 of 11

fortnightly and semi-annual modulations of the amplitudes deformations, the non-linear amplification due to the are visible. The fortnightly modulations result from neap exponential in Eq. (1) produces bias. and spring tides. Figure 2c shows the ΔCFSO and ΔCFSS+O between 1980 and 2013 at H1. At this horizontal scale, the The effects of non-tidal ocean loads on ΔCFS and slip rate semi-annual, 4.425- and 18.61-year modulations were To confirm the validity of the ocean model, Fig. 3a shows dominant. The variation in amplitudes of ΔCFSS+O over the monthly running average of the calculated OBP, which an 18.61-year cycle was between 10 and 20 %. is superimposed on Fig. 3 from Matsumoto et al. (2006). Figure 2d, e shows the slip rates obtained from the above Overall, our model, which is represented by the blue curve, value of ΔCFSS+O. In the hourly slip rate of (d), the non- reproduces the inter-annual tendencies of the observed linear amplification was remarkable, whereas the decadal OBP, except for the lower peaks in the model at approxi- variations in the slower slip rates near 2.5 cm/year were mately 2002.8 and 2002.9. smaller (i.e., the minimum slip rates were flatter) than Figure 3b shows the daily OBP from 1980 to 2013 cor- those in the larger slip rates of approximately 7 cm/year. responding to H2–6 from Fig. 1b. On the whole, the OBPs The peak-to-peak differences in the maximum slip rates at these sites were similar, except for their amplitudes. In a were approximately 5 and 10 mm/year for the 4.425- and closer examination of the time-series plots, the vari- 18.61-year periods, respectively, corresponding to 13 and ation patterns nearer the coast seemed to slightly differ 25 % of the assumed reference rate of 4 cm/year. Compar- from those farther from the coast. At H2, 4, and 6, the ing the hourly rate in (d) with the daily and monthly rates amplitudes were relatively large, and the increases in in (e), longer-period variations were more emphasized for OBP from 1988 to 1992 and 2000 to 2005 were clearer. the slip rates that were averaged over longer durations. At H3 and 5, which had smaller amplitudes, the increase In the monthly rate of (e), the difference in the ampli- corresponding to the latter period began in 2002. tude over 18.61 years was 0.3 mm/year. In addition, Decadal variations in the SSH along the Japanese coast at the average slip rate in the monthly rate of (e) was ap- mid-latitudes mainly result from westward propagations of proximately 0.9 mm/year faster than the assumed ref- Rossby waves, which are excited by changes in wind stress erence rate. In contrast with the case of ordinary tidal curl over the central North Pacific (e.g., Qiu and Chen

(a) (b)

(c)

Fig. 3 Non-tidal variations in ocean bottom pressure (OBP). a A comparison under equivalent water thickness to OBP. The blue line denotes the OBP estimated by the ocean model used in this study, which was developed by the Japan Meteorological Agency (Usui et al. 2006). The OBP was estimated at a longitude of 146°E and a latitude of 39.2°N. The red and black lines represent in situ observations from the OBPR-B site and another ocean model, respectively (Fig. 3 in Matsumoto et al. 2006). For easier comparison, the other plots were removed from the original figure in Matsumoto et al. (2006). b The daily OBP calculated by the JMA ocean model at the sites marked H2–6inFig.1b.Theorange curve on H2 denotes a 5-year running average. The superimposed pink bars denote periods of large-scale meandering of the Kuroshio Current, as reported by the JMA. It can be observed that the OBPs along the coast in the Tokai district increase (decrease) with the initiation (end) of the events. c Thesameas(b), but the OBP values from 1980 to 2013 are plotted cyclically against months Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 7 of 11

2010). Satellite altimeter data and the results from a A comparison of slip rate with seismicity of shallower numerical model together indicated that the SSH at a earthquakes longitude of 140°E and latitude of 32°–34°N increased Figure 4a shows the seismicity of the shallower earthquakes from 1989 to 1994 and 2001 to 2005 (Fig. 6b in Qiu that occurred between 1982 and 2010. The annual averages and Chen 2010). Figure 3b shows that these high SSH of the stress rates obtained from the slip rates in Fig. 2d,g anomalies correspond to high OBPs along the coast, are superimposed. which is more clearly visible in the 5-year running average When only the tidal effects were considered, the of the OBP at H2. stress rate was maximized between approximately 1988 With respect to OBP, shorter-term variations due to the and 2006, whereas three upper peaks appeared during large-scale meandering of the Kuroshio Current were also 1985, 1997, and 2007 when the non-tidal effects were observed. These periods are marked by pink bars (http:// included. When including the non-tidal effects, the stress www.data.jma.go.jp/kaiyou/data/shindan/b_2/kuroshio_- rate in 1997 was lower than the other two peaks, occurring stream/kuroshio_stream.html). The meandering began approximately in 1985 and 2007, which could not explain with the appearance of a stationary cold-water mass off the high seismicity observed from 1993 to 1999. However, the Kumano-nada (Okada 1978) (Fig. 1a). Figure 3b shows the decreased seismicity in approximately 1990 and 2005 that OBP increases when such meandering occurs. agreed well with the lower stress rate peaks in these Figure 2f shows the computed daily ΔCFSNT at H1. years, which were caused by meanderings of the Kuroshio When OBP was positive, ΔCFSNT was negative. The vari- Current. ation pattern in ΔCFSNT was similar to that at H2, 4, and 6, The overall agreement in phase between stress rate and reflecting the ocean loads nearer the coast more strongly. seismicity is a reminder of the fact that earthquakes are The amplitudes of ΔCFSNT in the decadal scales were more likely to be triggered near a phase with a maximum 50–100 Pa. It was also observed that ΔCFSNT rapidly stress rate, when the periodic stress disturbance is rela- increased after the meandering events of the Kuroshio tively small compared to the secular stress accumulation Current. A meandering event that started in 1935 and rate (Heki 2003). The epicenters of the inland events in lasted for approximately 10 years was previously reported Fig. 1 were located away from the plate interface, where (Okada 1978). The 1944 Tonankai and 1946 Nankaido the stress change caused by the fluctuating slip rate on the earthquakes occurred shortly after the end of this meand- plate interface might be attenuated. ering episode, which was consistent with the increase in ΔCFSNT. Figure 2g, h shows the slip rates obtained for the sum Seasonality of large earthquakes of ΔCFSS+O and ΔCFSNT. The 4.425-year modulation Figure 3c is a plot of the OBP during the period from 1980 was still visible in the hourly slip rates because ΔCFSNT to 2013, which is cyclic with respect to months. The time- was relatively small (Fig. 2g). In the long-term averages series plots at H2–6 indicate that the OBP tends to be of the slip rates (Fig. 2h), decadal variations in non- smaller from August to November. Figure 2c shows tidal effects were emphasized more, and their variation the corresponding daily ΔCFSNT, which peaks around patterns were similar to those of the OBP, as shown in September. Figure 4b shows monthly slip rates for the Fig. 3b. Moreover, when comparing the monthly slip cases including and excluding the non-tidal effects. When rate in Fig. 2h with the rate that was caused by only the considering only the tidal effects, the slip rates are highest tides (Fig. 2e), the fluctuation of the former was ap- in January and July. When adding the non-tidal effects, the proximately twice as large as the latter. The 18.61-year slip rates are larger around September. change in ΔCFSS+O mainly consists of modulations of The decreasing OBP and increasing slip rate in September diurnal and semi-diurnal oscillations, and the long- caused landward and seaward displacements, respectively, at term bias is almost constant with time. Thus, the con- the coastal GNSS stations. Both of these effects on displace- tributions of tides to long-term slip rates are effectively ments are expected to be less than 1 mm/year and to cancel smaller, despite their larger amplitudes over shorter periods each other out, which would be difficult to distinguish given (1–2 kPa). In contrast, slow changes in ΔCFSNT increase/ theprecisionoftheGNSSdata. decrease the decadal-scale slip rate effectively, even though The occurrence months of the great earthquakes the added non-tidal effects were only about 1/20th of the were closer to the periods when stress was maximized tidal ones (~0.05–0.1 kPa). (i.e., 3 months later than the phase of maximum slip rates), Incidentally, the fluctuation of the slip rate in region III, although the number of events is too small to find a clear where the ocean effects are much smaller than in region II, relationship (Fig. 4b). is mostly caused by solid earth tides (Fig. 2a). Consequently, The above example of seasonal scale also suggested the its long-term variation pattern becomes similar to Fig. 2d, e, importance of considering non-tidal effects when discuss- except that the amplitudes are slightly decreased. ing the relationship between slip rates and seismicity. Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 8 of 11

Fig. 4 A comparison between slip rates and seismicity. a The red solid line denotes the annual average of the slip rate in Fig. 2g, where the tidal and non-tidal effects are considered. The result is given in units of the rate of stress change by multiplying the slip rates by an elastic constant, based on Eq. (2). A 5-year running average is also superimposed to emphasize the decadal variations. The blue curve denotes the annual average of the rate of stress change, computed from the slip rate shown in Fig. 2d, where only the tidal effects are considered. The yellow circles denote the background seismicity, inferred by the method of Ide (2013). The employed earthquakes are shown in Fig. 1c,d. The superimposed pink bars denote periods of large-scale meandering of the Kuroshio Current, as in Fig. 3b, during which the seismicity seemed to decrease. When excluding non-tidal effects, the increase in seismicity during the mid-1990s cannot be explained. b The horizontal and vertical axes denote months and slip rate, respectively. The red and blue symbols denote the monthly averages in Fig. 2h,e, respectively, from 1980 to 2013, which are plotted cyclically against months. The green line represents the frequency of great historical earthquakes in the Tokai area (1605, 1707, and 1854), for which Mogi (1969) noted the seasonality. c The red and blue curves denote the stress changes obtained by integrating the rates in Fig. 2g with respect to time. The purple bars show the periods when four long-term slow slip events occurred in the Tokai area (Kobayashi 2014; Geographical Information Authority of Japan 2015). d The red and blue curves denote the slip rates for cases including and excluding non-tidal effects, respectively, when A − B is assumed to be negative (see text). The purple bars show the periods of the SSEs

Comparing slip rate with long-term SSEs a rapid rupture, a frictional law, such as in Matsuzawa et al. Compared to the stress rate in Fig. 4a, SSE initiation seems (2010), is implicitly assumed. to be delayed by 3–4 years. According to Heki (2003), when For example, Fig. 4d shows slip rates for cases including/ a stress disturbance is larger, earthquakes are more likely to excluding non-tidal effects when A − B=−2kPa.When be triggered under maximum stress. SSEs occur on plate considering only tidal effects, the long-term rates possessed interfaces and therefore should be more strongly affected a similar pattern to those in the case with a positive A − B by slip rate fluctuations on the plate interface than shal- (Fig. 4c) because the long-term slip rates became faster lower inland events. To confirm this, Fig. 4c shows the when the diurnal and semi-diurnal tidal amplitudes were stress change obtained by integrating the hourly slip rate in larger. When adding non-tidal effects, the rate became Fig. 2g with respect to time. The stress became rela- larger from 1988 to 1991, 1999 to 2005, and 2010 to tively large from 1986 to 1991, 1998 to 2002, and 2007 2013. The SSEs in 1988, 2000, and 2013 occurred dur- to 2013. Except for the first event, which possessed a ing or near periods with faster slip rates. For the earliest smaller moment magnitude (Kobayashi 2014), the three event, which occurred from 1980 to 1982, the correlation events seemed to initiate 2–4 years after the computed was unclear due to the lack of pre-1980 data. stress reached a maximum. The cause behind the de- However, the increase in slip rate from 2000 to 2005 was layed onsets of the SSEs is not clear. More events are approximately 0.5 mm/year, which was more than an order necessary to confirm whether a weak correspondence be- of magnitude smaller than the observed slip rate for the tween stress and SSE initiation continues in the future. 2000 event (Fig. 14 of Suito and Ozawa 2009). Thus, a direct response to external tidal and non-tidal stresses cannot Can SSEs be interpreted by pure responses to external forces? explain the SSE when considering the magnitude of the In this section, a hypothetical case of region II having a frictional parameter that was determined by observing negative A − B is considered. In this case, the slip rate tremors (2 kPa). To interpret the SSE as a direct response represented by Eq. (1) for i = 2 could be interpreted as of the slow slip area to external stresses using our model, slow slip. To prevent the slow slip from developing into A − B must be even smaller. Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 9 of 11

If the value of A − B is correct, then to interpret the discussed in the “Method for computing slip rate” (denoted SSE as a direct response, a mechanism is necessary in by Dc) depends on the scale of irregularities, such that which the slip rate is amplified. One possibility may in- smaller (larger) irregularities have shorter (longer) charac- volve the effect of random noises on the system. Once teristic distances (e.g., Matsu’ura et al. 1992). The charac- the slip rate begins to increase, the effects of local stress teristic time of the decay of the state variable can be disturbances caused by microfractures and episodic slow approximated as Dc/V,whereV is the slip rate. It fol- events to promote the slip are more easily increased by lows that large-scale irregularities have longer charac- non-linear effects. If these disturbances occur randomly teristic times when the slip rate is the same. Therefore, in time and their amplitudes are larger than the fluctuations the effects of slower stress disturbances caused by decadal- caused by tidal and non-tidal effects, so-called stochastic scale modulations of the state variable would persist for resonance occurs, which would emphasize the effects longer on larger asperities. Tidal and non-tidal varia- of smaller disturbances with slower time scales. To tions have long wavelengths, which change the stress confirm this, however, an earthquake cycle simulation over an asperity, corresponding to a megathrust event. study that incorporates external forces and noises is Han et al. (2014) showed that tremors and slow slips can necessary. trigger small earthquakes. At small spatial scales, local stress changes caused by such slow events occur more A note on the periodicity of large earthquakes and the PDO frequently and are more dominant than long-term stress A possible periodicity in historical large earthquakes disturbances caused by tides and non-tidal effects, which in Japan Thus far, the importance of non-tidal modula- may result in less clear correlations with decadal-scale tions in estimating slip fluctuations has been demon- modulations. strated, and the purpose of this study has been attained. In this section, some decadal time-scale phenomena, Can the PDO be related to the occurrence of large which seem to be related to tidal and non-tidal modula- earthquakes? Although there are insufficient evidences tions, are introduced to provide material for future studies to answer this question, a working assumption could be to help elucidate decadal triggering mechanisms of large made. When the PDO index is positive, negative SSH earthquakes. anomalies are created in the eastern North Pacific. These Tanaka (2014) reported a possible historical periodicity anomalies propagate west over 3–4 years and decrease the for earthquakes with M > 7.5 in northeast Japan. The epi- SSH along the Japanese coast at mid-latitudes. Recent centers of 22 events are shown in Fig. 1a. The reasons for negative SSH anomalies were observed in approximately choosing these events and the risks of using incomplete 1998 and 2008 at a longitude of 140° (Fig. 6 in Qiu and historical data are described in detail by Tanaka (2014). Chen 2010). These periods corresponded to lower OBPs The periodicities were investigated for 8.85 and 18.61 years and faster rates of stress change in region I, when A − B in associated with extremely weak tides. Figure 3b,e in region II is positive (Fig. 4a). The 8.85-year peak in seismi- Tanaka’s paper shows relatively strong and weak corre- city found in historical large earthquakes corresponds to lations for the 8.85 and 18.61 year periods, respect- T = 2011.7 − 8.85n (year), where n is an integer number ively. If the principle of superposition holds, then the (Fig. 3c in Tanaka 2014). The two recent periods (2011.7 effects of these two periods should be combined when and 2002.9) were delayed by 4–5 years from periods with constructing a histogram to test periodicity. However, lower OBPs. The stress changes reached maximums ap- to define periods with greater stress, a stress threshold proximately 2.5 years after 1998 and 2008, when the period above which earthquakes are more likely to be triggered of disturbance was 10 years. If differences of 1–2 years are must be set for combined disturbances consisting of larger allowed,itmaybepossiblethatthepeakoftheseismicity and smaller peaks. Such a threshold would depend on the corresponded to a period when stress was at a maximum. amplitude of each disturbance, which is unknown. To avoid Scafetta and Mazzarella (2015) reported that the PDO such uncertainties, the two periods were treated separately. index and a world historical earthquake record had com- mon spectral peaks at approximately 5.7, 8.9, and 20 years. Why do larger earthquakes show stronger correlations? Yasuda (2009) found that 18.61-year tides have been corre- The hypothesis that fluctuations in subduction speed lated with the historical PDO index since the eighteenth in the transition zone affect the seismicity of shallower century. Therefore, the 20-year peak found by Scafetta and earthquakes seems to hold for earthquakes of all mag- Mazzarella (2015) might be related to the 18.61-year tides. nitudes. However, smaller events tend to show weaker The mechanisms generating the other spectral peaks in the correlations with long-termtidalperiods(Fig.3c,gin PDO index have not been revealed. The long-term stability Tanaka 2014). of the phase of the periodic variation in seismicity along The lower correlations shown by smaller earthquakes the Japan Trench could indicate that not only the 18.61- could be qualitatively explained if the characteristic distance year but also the 8.85- and 4.425-year tidal modulations Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 10 of 11

are connected with the generation of PDO. However, be key toward improving the ocean model. In situ and 8.85-year tidal modulations are weaker than 4.425-year satellite observations, climatology, and oceanography modulations (e.g., Haigh et al. 2011). Thus, the fact that will be helpful in providing more accurate estimates of approximately 8.85-year variations are more remarkable external stress disturbances for use as inputs in nu- than 4.425-year variations in the seismicity and the PDO merical simulations. index is mysterious. Abbreviations The dominance of the 8.85-year variations in seismicity CFS: Coulomb fracture stress; GNSS: global navigation satellite system; could be explained if the characteristic distance mentioned OBP: ocean bottom pressure; PDO: Pacific Decadal Oscillation; SSE: slow slip above depended on the scale of irregularities (i.e., longer event; SSH: sea surface height. disturbances survive longer). For the PDO index, it is ex- Competing interests pected that oceanographic studies will elucidate the origin The authors declare that they have no competing interests. of the approximately 9-year variation to confirm whether ’ the periodicity of historical large events is real. Authors contributions YT designed the study, calculated the stress and slip rates, analyzed the earthquake data, and wrote the manuscript. SY computed the stress and Conclusions analyzed tremors. SI modeled the slip rates and analyzed the tremor and The long-term fluctuations in subduction speed due to earthquake data. All authors read and approved the final manuscript. tidal and non-tidal modulations in the Tokai slow slip Acknowledgements area were estimated using an empirical slip response model, The Japan Meteorological Agency (JMA) earthquake catalogue was used in under the assumption that the effects of stress disturbances this study. The ocean model was provided by the oceanography and geochemistry research department of the Meteorological Research Institute on the slow slip area are dominant in changing inter-plate (MRI) at the JMA. We acknowledge Dr. Tomoki Tozuka, Daisuke Inazu, and coupling and that variations in the state variable are small. Yuki Tanaka at the University of Tokyo and Tamaki Yasuda and Norihisa Usui Non-tidal effects on the long-term slip fluctuations are lar- at MRI for their valuable comments regarding the ocean. The manuscript was greatly improved by the insightful comments from the reviewers Dr. ger than tidal effects in areas covered by the ocean, such as Kosuke Heki and Heidi Houston. Tokai, and non-tidal contributions should not be neglected when discussing temporal coincidences between obtained Author details 1Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku slip rates and seismicity. 113-0032, Tokyo. 2Department of Earth and Planetary Science, University of Absolute amplitudes of estimated slip rates depend on Tokyo, 7-3-1 Hongo, Bunkyo-ku 113-0033, Tokyo. frictional parameters. Assuming that the effective nor- Received: 22 February 2015 Accepted: 20 August 2015 mal stress is as low as in the tremor zone, long-term slip rate fluctuations could reach 1 mm/year, suggesting the possibility that the parameters could be constrained by References Agnew, DC (2012) SPOTL: Some Programs for Ocean-Tide Loading, SIO Technical crustal deformation data. However, the fluctuation am- Report, Scripps Institution of Oceanography, http://escholarship.org/uc/item/ plitudes were more than an order of magnitude smaller 954322pg than the slip rates for past SSEs, and it was not possible Baba T, Tanioka Y, Cummins PR, Uhira K (2002) The slip distribution of the 1946 Nankai earthquake estimated from tsunami inversion using a new plate to interpret the slip rate fluctuation of an SSE unless the model. Phys Earth Planet Inter 132:59–73 effective normal stress was even smaller. Beeler NM, Lockner DA (2003) Why earthquakes correlate weakly with the solid To determine whether changes in shear stress result- earth tides: effects of periodic stress on the rate and probability of earthquake occurrence. J Geophys Res 108:2391. doi:10.1029/2001JB001518 ing from fluctuations in slip rate can trigger slow events Beroza GC, Ide S (2011) Slow earthquakes and non-volcanic tremor. Ann Rev and earthquakes, our model, which was used to evaluate Earth Planet Sci 39:271–296 external stresses, is oversimplified. For example, it is neces- Dragert H, Wang K, Rogers G (2004) Geodetic and seismic signatures of episodic tremor and slip in the northern Cascadia subduction zone. Earth Planets sary to consider interactions between the transition zone Space 56:1143–1150 and locked zones based on a rate- and state-dependent fric- Dziewonski AM, Anderson A (1981) Preliminary reference earth model. Phys Earth tional law (e.g., Matsuzawa et al. 2010; Shibazaki et al. 2011; Planet Inter 25:297–356 Geographical Information Authority of Japan (2015) Crustal movements in the Hirose and Maeda 2013; Hori et al. 2014). Tokai district, Report of the Coordinating Committee for Earthquake To perform such simulation studies, it is important to in- Prediction. Japan 93:175–226 (in Japanese with English figure captions) clude both non-tidal and tidal effects. In this study, OBP Haigh ID, Eliot M, Pattiaratchi C (2011) Global influences of the 18.61 year nodal cycle and 8.85 year cycle of lunar perigee on high tidal levels. J Geophys Res was evaluated with an ocean model to assimilate observed 116:C06025. doi:10.1029/2010JC006645 atmospheric and oceanographic data. In situ observations Han J, Vidale JE, Houston H, Chao K, Obara K (2014) Triggering of tremor and of OBP (e.g., Ito et al. 2013) have occurred in only recent inferred slow slip by small earthquakes at the Nankai subduction zone in southwest Japan. Geophys Res Lett 41:8053–8060. doi:10.1002/2014GL061898 history, such that wide-area annual variation patterns have Heki K (2003) Snow load and seasonal variation of earthquake occurrence in not been adequately revealed. On the other hand, a Japan, Earth planet. Sci Lett 207:159–164 regional-scale OBP was revealed by a satellite gravity Heki K (2004) Dense GPS array as a new sensor of seasonal changes of surface loads, in The State of the Planet: Frontiers and Challenges in Geophysics, Vol. mission (e.g., Petrick et al. 2014). Assimilating obser- 150, pp. 177–196, eds Sparks, R.S.J. & Hawkesworth, C.J., Geophys. vations with such different space-time resolutions will Monograph, American Geophysical Union, Washington Tanaka et al. Earth, Planets and Space (2015) 67:141 Page 11 of 11

Hirose F, Maeda K (2013) Simulation of recurring earthquakes along the Nankai Okada M (1978) History of the large meander of the Kuroshio (1854—1977) and trough and their relationship to the Tokai long-term slow slip events taking sea level observations. Marine Sciences Quarterly 1:81–88 (in Japanese) into account the effect of locally elevated pore pressure and subducting Okada Y (1992) Internal deformation due to shear and tensile faults in a ridges. J Geophys Res 118:1–18. doi:10.1002/jgrb.50287 half-space. Bull Seism Soc Am 82:1018–1040 Hirose F, Nakajima J, Hasegawa A (2008) Three-dimensional seismic velocity Okubo S, Tsuji D (2001) Complex Green’s function for diurnal/semidiurnal loading structure and configuration of the Philippine Sea slab in southwestern Japan problems. J Geodetic Soc Japan 47:225–230 estimated by double-difference tomography. J Geophys Res 113:B09315. Onogi K, Tsutsui J, Koide H, Sakamoto M, Kobayashi S, Hatsushika H, Matsumoto doi:10.1029/2007JB005274 T, Yamazaki N, Kamahori H, Takahashi K, Kadokura S, Wada K, Kato K, Oyama Hori T, Hyodo M, Nakata R, Miyazaki S, Kaneda Y (2014) A forecasting procedure R, Ose T, Mannoji N, Taira R (2007) The JRA-25 Reanalysis. J Meteorol Soc for plate boundary earthquakes based on sequential data assimilation. Japan 85:369–432 Oceanography 27(2):94–102, http://dx.doi.org/10.5670/oceanog.2014.44 Peacock SM (2009) Thermal and metamorphic environment of subduction zone Houston H (2015) Low friction and fault weakening revealed by rising sensitivity episodic tremor and slip. J Geophys Res 114:B00A07. doi:10.1029/2008JB005978 of tremor to tidal stress. Nat Geosci 8:409–415. doi:10.1038/ngeo2419 Petrick C, Dobslaw H, Bergmann-Wolf I, Schon N, Matthes K, Thomas M (2014) 552 Ide S (2013) The proportionality between relative plate velocity and seismicity in Low-frequency ocean bottom pressure variations in the North Pacific in response subduction zones. Nat Geosci 6:780–784. doi:10.1038/ngeo1901 to 553 time-variable surface winds. J Geophys Res Oceans 119(5190–5202):554. Ide S, Tanaka Y (2014) Controls on plate motion by oscillating tidal stress: evidence doi:10.1002/2013JC009635 from deep tremors in western Japan. Geophys Res Lett 41:3842–3850. Pollitz FF, Wech A, Kao H, Bürgmann R (2013) Annual modulation of non-volcanic doi:10.1002/2014GL060035 tremor in northern Cascadia. J Geophys Res Solid Earth 118:2445–2459. Ide S, Beroza GC, Shelly DR, Uchide T (2007a) A scaling law for slow earthquakes. doi:10.1002/jgrb.50181 Nature 447:76–79 Pugh DT (1987) Tides, surges and mean sea level, vol 488. John Wiley, Chichester, U. K Ide S, Shelly DR, Beroza GC (2007b) Mechanism of deep low frequency earthquakes: Qiu B, Chen S (2010) Eddy-mean flow interaction in the decadally modulating further evidence that deep non-volcanic tremor is generated by shear slip on the Kuroshio Extension system. Deep-Sea Research II, doi:10.1016/j.dsr2.2008.11.036 plate interface. Geophys Res Lett 34:L03308. doi:10.1029/2006GL028890 Rubinstein JL, La Rocca M, Vidale JE, Creager KC, Wech AG (2008) Tidal modulation of Idehara K, Yabe S, Ide S (2014) Regional and global variations in the temporal nonvolcanic tremor. Science 319:186–189. doi:10.1126/science.1150558 clustering of tectonic tremor activity. Earth, Planets and Space 66:66. Scafetta N, Mazzarella A (2015) Spectral coherence between climate oscillations doi:10.1186/1880-5981-66-66 and the M ≥ 7 earthquake historical worldwide record, Natural Hazards, in Ito Y, Hino M, Kido H, Fujimoto H, Osada Y, Inazu Y, Ohta Y, Linuma T, Ohzono M, press, DOI 10.1007/s11069-014-1571-z Miura S, Mishima M, Suzuki K, Tsuji T, Ashi J (2013) Episodic slow slip events Scholz CH (2002) The mechanics of earthquakes and faulting, vol 496, 2nd edn. in the Japan subduction zone before the 2011 Tohoku-Oki earthquake. Cambridge University Press, Cambridge Tectonophysics 600:14–26 Schwartz SY, Rokosky JM (2007) Slow slip events and seismic tremor at circum-Pacific Kataoka T (2007) Correlation Between Annual Variation of Ocean Bottom subduction zones. Rev Geophys 45:RG3004. doi:10.1029/2006RG000208 Pressure and Seasonality of Great Earthquake Occurrences Along the Segall P, Bradley AM (2012) Slow-slip evolves into megathrust earthquakes in 2D Nankai and Sagami Troughs. BSc thesis, School of Science, Hokkaido numerical simulations, Geophys Res Lett., 39 (18), doi:10.1029/2012GL052811 University (in Japanese) Shelly DR, Beroza GC, Ide S, Nakamula S (2006) Low-frequency earthquakes in Kobayashi A (2014) A long-term slow slip event from 1996 to 1997 in the Kii Shikoku, Japan, and their relationship to episodic tremor and slip. Nature – Channel. Japan, Earth Planets and Space 66:9. doi:10.1186/1880-5981-66-9 442:188 191 Kodaira S, Iidaka T, Kato A, Park JO, Iwasaki T, Kaneda Y (2004) High pore fluid Shelly DR, Beroza GC, Ide S (2007) Non-volcanic tremor and low-frequency – pressure may cause silent slip in the Nankai Trough. Science 304:1295–1298 earthquake swarms. Nature 446:305 307 Lambert A, Kao H, Rogers G, Courtier N (2009) Correlation of tremor activity with Shibazaki B, Matsuzawa T, Tsutsumi A, Ujiie K, Hasegawa A, Ito Y (2011) 3D tidal stress in the northern Cascadia subduction zone. J Geophys Res modeling of the cycle of a great Tohoku-oki earthquake, considering 114:B00A08. doi:10.1029/2008JB006038 frictional behavior at low to high slip velocities. Geophys Res Lett 38:L21305. Matsu’ura M, Kataoka H, Shibazaki K (1992) Slip-dependent friction law and nucleation doi:10.1029/2011GL049308 – processes in earthquake rupture. Tectonophysics 211:135–148 Suito H, Ozawa S (2009) Transient crustal deformation in the Tokai district The Tokai slow slip event and postseismic deformation caused by the 2004 off Matsumoto K, Sato T, Takanezawa T, Ooe M (2000) GOTIC2: a program for – computation of oceanic tidal loading effect. J Geod Soc Jpn 47:243–248 Southeast Kii Peninsula Earthquakes. J Seism Soc Jap 2nd ser 61:113 135, in Japanese with an English abstract Matsumoto K, Sato T, Fujimoto H, Tamura Y, Nishino M, Hino R, Higashi T, Tamura Y (1987) A harmonic development of the tide generating potential. Bull Kanazawa T (2006) Oceanbottom pressure observation off Sanriku and Inf Marées Terrestres 99:6813–6855 comparison with ocean tide models, altimetry, and barotropic signals from Tanaka Y (2014) An approximately 9-yr-period variation in seismicity and crustal ocean models. Geophys Res Lett 33:L16602. doi:10.1029/2006GL026706 deformation near the Japan Trench and a consideration of its origin. Matsuzawa T, Hirose H, Shibazaki B, Obara K (2010) Modeling short- and long- Geophys J Int 196:760–787. doi:10.1093/gji/ggt424 term slow slip events in the seismic cycles of large subduction earthquakes. Tsuruoka H, Ohtake M, Sato H (1995) Statistical test of the tidal triggering of J Geophys Res 115:B12301. doi:10.1029/2010JB007566 earthquakes: contribution of the ocean tide loading effect. Geophys J Int Miyazawa M, Mori J (2006) Evidence suggesting fluid flow beneath Japan due to 122:183–194 periodic seismic triggering from the 2004 Sumatra-Andaman earthquake. Usui N, Ishizaki S, Fujii Y, Tsujino H, Yasuda T, Kamachi M (2006) Meteorological Geophys Res Lett 33:L05303. doi:10.1029/2005GL025087 Research Institute multivariate ocean variational estimation (MOVE) system: Mogi K (1969) Monthly distribution of large earthquakes in Japan. Bull Earthq Res some early results. Adv Space Res 37:806–822. doi:10.1016/j.asr.2005.09.022 Inst 47:419–427 Vidale JE, Houston H (2012) Slow slip: a new kind of earthquakes. Phys Today Nagata K, Nakatani M, Yoshida S (2012) A revised rate- and state-dependent 65:38–43 friction law obtained by constraining constitutive and evolution laws Yabe S, Ide S, Tanaka Y, Houston H (2014) Tidal stress influence on the deep separately with laboratory data. J Geophys Res 117:B02314. doi:10.1029/ plate interface, AGU fall meeting, S52B-05, 19 Dec., San Francisco, USA 2011JB008818 Yasuda I (2009) The 18.6-year period moon-tidal cycle in Pacific Decadal Nakajima J, Hasegawa A (2007) Subduction of the Philippine Sea plate beneath Oscillation reconstructed from tree-rings in western North America. Geophys southwestern Japan: Slab geometry and its relationship to arc magmatism. Res Lett 36:L05605. doi:10.1029/2008GL036880 J Geophys Res 112:B08306. doi:10.1029/2006JB004770 Nakata R, Suda N, Tsuruoka H (2008) Non-volcanic tremor resulting from the combined effect of Earth tides and slow slip events. Nat Geosci 1:676–678 Obara K (2002) Nonvolcanic deep tremor associated with subduction in southwest Japan. Science 296:1679–1681 Ohtake M, Nakahara H (1999) Seasonality of great earthquake occurrence at the northwestern margin of the Philippine Sea Plate. Pure Appl Geophys 155:689–700